(81/16)^{025}*((-8)^-frac{4{3}}*a^-8)*(2^-2*a^30)= eching

$$( \frac { 81 } { 16 } ) ^ { 025 } \cdot ( ( - 8 ) ^ { - \frac { 4 } { 3 } } \cdot a ^ { - 8 } ) \cdot ( 2 ^ { - 2 } \cdot a ^ { 30 } ) =$$

Baholash

$$\frac{a^{22}}{64}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -8 va 30 ni qo‘shib, 22 ni oling.

$$\left(\frac{81}{16}\right)^{0\times 25}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2}$$

0 hosil qilish uchun 0 va 25 ni ko'paytirish.

$$\left(\frac{81}{16}\right)^{0}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2}$$

0 daraja ko‘rsatkichini \frac{81}{16} ga hisoblang va 1 ni qiymatni oling.

$$1\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2}$$

-\frac{4}{3} daraja ko‘rsatkichini -8 ga hisoblang va \frac{1}{16} ni qiymatni oling.

$$1\times \frac{1}{16}a^{22}\times 2^{-2}$$

\frac{1}{16} hosil qilish uchun 1 va \frac{1}{16} ni ko'paytirish.

$$\frac{1}{16}a^{22}\times 2^{-2}$$

-2 daraja ko‘rsatkichini 2 ga hisoblang va \frac{1}{4} ni qiymatni oling.

$$\frac{1}{16}a^{22}\times \frac{1}{4}$$

\frac{1}{64} hosil qilish uchun \frac{1}{16} va \frac{1}{4} ni ko'paytirish.

$$\frac{1}{64}a^{22}$$

a ga nisbatan hosilani topish

$$\frac{11a^{21}}{32}$$

Derivativ ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -8 va 30 ni qo‘shib, 22 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(\frac{81}{16}\right)^{0\times 25}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2})$$

0 hosil qilish uchun 0 va 25 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(\frac{81}{16}\right)^{0}\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2})$$

0 daraja ko‘rsatkichini \frac{81}{16} ga hisoblang va 1 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(1\left(-8\right)^{-\frac{4}{3}}a^{22}\times 2^{-2})$$

-\frac{4}{3} daraja ko‘rsatkichini -8 ga hisoblang va \frac{1}{16} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(1\times \frac{1}{16}a^{22}\times 2^{-2})$$

\frac{1}{16} hosil qilish uchun 1 va \frac{1}{16} ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{16}a^{22}\times 2^{-2})$$

-2 daraja ko‘rsatkichini 2 ga hisoblang va \frac{1}{4} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{16}a^{22}\times \frac{1}{4})$$

\frac{1}{64} hosil qilish uchun \frac{1}{16} va \frac{1}{4} ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{64}a^{22})$$

ax^{n} hosilasi – nax^{n-1}.

$$22\times \frac{1}{64}a^{22-1}$$

22 ni \frac{1}{64} marotabaga ko'paytirish.

$$\frac{11}{32}a^{22-1}$$

22 dan 1 ni ayirish.

$$\frac{11}{32}a^{21}$$